Item-sensitivity, defined as whether a model's choice depends on the specific input rather than on its own output prior, is widely reported as evidence of task competence. We show this evidence is necessary but not sufficient using a forced-choice signalling task abstracted from the board game Deception: Murder in Hong Kong. In this environment, the reference points against which a coordinate should be judged (a fit-maximising strategy, a posterior-maximising strategy, and uniform random selection) are all computable in closed form. Across seven language models, two model families, a post-training ablation, and three independent scoring rules, every one of 21 model-by-rule cells is reliably item-sensitive. Yet 8 of those 21 cells are not statistically distinguishable from a chooser that ignores the item and selects at random, and 5 score worse than random at describing the target. Item-sensitivity and distance from random correlate at only r = 0.30. We call this consistency without alignment and argue it generalises to any evaluation that relies on item-sensitivity, permutation consistency, or self-consistency without an independent reference for the measured quantity. We further find that a literal-similarity baseline with no pragmatics outperforms most tested language models, that adding a pragmatic layer over two baseline similarity sources moves choosers toward random rather than toward the Bayesian reference, and that a standard labelled multiple-choice format carries no measurable content signal here. All results represent the model side of a pre-registered instrument; a matched human condition is designed and piloted but not yet collected.

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